Statistics: nonparametric test with heterogeneity of variance

Hi.

I have a basic statistics question. I want to find the test that is most applicable for comparing two groups. Those groups are assumed to be random and independent. In most cases, the groups are not normally distributed and homogeneity of variance (or similarity of shape) is not always guaranteed. I am not sure which statistic test to use in this kind of situation. Maybe someone has an idea?

(The Mann-Whitney-Wilcoxon test for example does assume that the groups have a similar distributional shape, so I am violating the assumption if I use it).